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Results tagged with quadratic-residues
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user 18494
1
vote
Irreducibility of polynomials related to quadratic residues
Regarding the Galois group of the factor $g(x)=g(q,x)$of these Fekete polynomials that is conjectured to be irreducible, here is PARI code that counts, for each prime $q \equiv 1 \bmod 4$, $17 \leq q …
4
votes
0
answers
327
views
Shortest interval over which there are more quadratic residues than nonresidues
Hi, I refer to formula (8) in Chapter 1 of H. Davenport, Multiplicative Number Theory, Third Edition, Springer (2000), which says that for primes $q\equiv 3 \bmod 4$:
$$
L\left(\left(\frac{\cdot}{q}\ …
- 1,075
4
votes
Irreducibility of polynomials related to quadratic residues
Hi,
In Remark 2 of "Zeros of Fekete Polynomials", (http://arxiv.org/PS_cache/math/pdf/9906/9906214v1.pdf), Conrey et. al. give
$$\sup_{|z|=1}|f(z)| \ll p^{0.5} \log p.$$
But the Mahler measure of $f …
- 1,075